Simulated Quantum Computation of Global Minima

TL;DR

This paper demonstrates that a modified Grover's quantum algorithm can efficiently find global minima in optimization problems, reducing the number of function evaluations significantly and enabling larger system analysis when combined with classical methods.

Contribution

The paper introduces a modified Grover's quantum algorithm for global optimization and shows its effectiveness on test functions and clusters, combining it with classical methods for larger problems.

Findings

Reduced function evaluations from O(N) to O(√N) using quantum algorithm.

Successful application to Lennard-Jones clusters and test functions.

Enhanced optimization capability when combined with classical Pivot method.

Abstract

Finding the optimal solution to a complex optimization problem is of great importance in practically all fields of science, technology, technical design and econometrics. We demonstrate that a modified Grover's quantum algorithm can be applied to real problems of finding a global minimum using modest numbers of quantum bits. Calculations of the global minimum of simple test functions and Lennard-Jones clusters have been carried out on a quantum computer simulator using a modified Grover's algorithm. The number of function evaluations $N$ reduced from O(N) in classical simulation to $O(\sqrt{N})$ in quantum simulation. We also show how the Grover's quantum algorithm can be combined with the classical Pivot method for global optimization to treat larger systems.